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Search: id:A133457
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| A133457 |
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Irregular triangle read by rows: row n gives exponents in expression for n as a sum of powers of 2. |
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+0
2
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| 0, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 2, 3, 0, 3, 1, 3, 0, 1, 3, 2, 3, 0, 2, 3, 1, 2, 3, 0, 1, 2, 3, 4, 0, 4, 1, 4, 0, 1, 4, 2, 4, 0, 2, 4, 1, 2, 4, 0, 1, 2, 4, 3, 4, 0, 3, 4, 1, 3, 4, 0, 1, 3, 4, 2, 3, 4, 0, 2, 3, 4, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 0, 5, 1, 5, 0, 1, 5, 2, 5, 0, 2, 5, 1, 2, 5, 0, 1, 2, 5, 3, 5, 0, 3, 5
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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This sequence contains every increasing finite sequence. For example, the finite sequence {0,2,3,5} arises from n = 45.
Essentially A030308(n,k)*k, then entries removed where A030308(n,k)=0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
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EXAMPLE
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1 = 2^0
2 = 2^1
3 = 2^0 + 2^1
4 = 2^2
5 = 2^0 + 2^2
etc. and reading the exponents gives the rows of the triangle.
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MAPLE
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A133457 := proc(n) local a, bdigs, i ; a := [] ; bdigs := convert(n, base, 2) ; for i from 1 to nops(bdigs) do if op(i, bdigs) <> 0 then a := [op(a), i-1] ; fi ; od: a ; end: seq(op(A133457(n)), n=1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
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CROSSREFS
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Cf. A067255.
Sequence in context: A127543 A068907 A033687 this_sequence A068067 A046926 A074398
Adjacent sequences: A133454 A133455 A133456 this_sequence A133458 A133459 A133460
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KEYWORD
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base,tabf,easy,nonn
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AUTHOR
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Masahiko Shin (nin-ts5406(AT)w9.dion.ne.jp), Nov 27 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
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